From the Mayer-Vietoris spectral sequence to berhomology

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS(2023)

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摘要
We prove that the second page of the Mayer-Vietoris spectral sequence, with respect to anti-star covers, can be identified with another homological invariant of simplicial complexes: the $0$-degree uberhomology. Consequently, we obtain a combinatorial interpretation of the second page of the Mayer-Vietoris spectral sequence in this context. This interpretation is then used to extend the computations of bold homology, which categorifies the connected domination polynomial at $-1$.
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关键词
Mayer-Vietoris spectral sequence,uberhomology,domination polynomial
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